SOLUTION: How do I write the equation of the ellipse {{{9x^2 + 4y^2 - 36x + 24y + 36 = 0}}} in standard form? Thank-you!

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Question 269783: How do I write the equation of the ellipse in standard form? Thank-you!
Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
Here is our equation

step 1 - rearrange so that x's are together and y's are together as

step 2 - complete the square on both x's and y's to get

The blanks are waiting for numbers . . .
step 3 - take (1/2) middle term and square it. PUt these into the left side of blanks as

we added 4 into the x's, but there is a 9 in front, so we really added 36. add 36 to the right side to keep it balanced.
we added 9 into the y's, but there is a 4 in front, so we really added 36. add another 36 to the right side to keep it balanced. we get

step 4 - rewrite the left side as 2 binomials squared and simplify the right side as

step 5 - divide by 36 to get